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I keep thinking that if I fail my Qual exams and don't become a Math Ph.D. that I'll switch over to the Philosophy department and study the philosophy of science. Then I'll write books like Michael Shermer and Steven Pinker.
Have you read any Karl Popper? I think that guy rocks, although his works are rather large, so it'd take ages to get through any of it.
Philosophy of science is, in my opinion, an underappreciated area, and we need loads more scientists contributing. Though you sound like you'll do well in the quals, going over to philosophy wouldn't be all that bad. A representative from the female mathematicians would be excellent. By the way, hi :)
Haven't read any Popper. Sigh. It's sad to think about "reading for pleasure" right now. I can't do it because I feel like I should be studying instead. Maybe in September.
As far as PhilScience goes, yes, definitely undervalued. My favorite two philosophy classes (of which I took many!) were the Philosophy of Psychology and the Philosophy of Biology taught by a PhilScience professor who was amazing. My university even has a couple philosophers interested in the philosophy of mathematics. I had hoped to take some of their classes "in my spare time" as a graduate student. Unfortunately, the math department looks down on this sort of strongly. | ||||||||||||||||||||||||||||||||